<!doctype html>
<html>
<head>
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>

<link href='https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text/css' /><style type='text/css'>html {overflow-x: initial !important;}:root { --bg-color:#ffffff; --text-color:#333333; --select-text-bg-color:#B5D6FC; --select-text-font-color:auto; --monospace:"Lucida Console",Consolas,"Courier",monospace; --title-bar-height:20px; }
.mac-os-11 { --title-bar-height:28px; }
html { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }
body { margin: 0px; padding: 0px; height: auto; inset: 0px; font-size: 1rem; line-height: 1.42857; overflow-x: hidden; background: inherit; tab-size: 4; }
iframe { margin: auto; }
a.url { word-break: break-all; }
a:active, a:hover { outline: 0px; }
.in-text-selection, ::selection { text-shadow: none; background: var(--select-text-bg-color); color: var(--select-text-font-color); }
#write { margin: 0px auto; height: auto; width: inherit; word-break: normal; overflow-wrap: break-word; position: relative; white-space: normal; overflow-x: visible; padding-top: 36px; }
#write.first-line-indent p { text-indent: 2em; }
#write.first-line-indent li p, #write.first-line-indent p * { text-indent: 0px; }
#write.first-line-indent li { margin-left: 2em; }
.for-image #write { padding-left: 8px; padding-right: 8px; }
body.typora-export { padding-left: 30px; padding-right: 30px; }
.typora-export .footnote-line, .typora-export li, .typora-export p { white-space: pre-wrap; }
.typora-export .task-list-item input { pointer-events: none; }
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}
#write li > figure:last-child { margin-bottom: 0.5rem; }
#write ol, #write ul { position: relative; }
img { max-width: 100%; vertical-align: middle; image-orientation: from-image; }
button, input, select, textarea { color: inherit; font: inherit; }
input[type="checkbox"], input[type="radio"] { line-height: normal; padding: 0px; }
*, ::after, ::before { box-sizing: border-box; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p, #write pre { width: inherit; }
#write h1, #write h2, #write h3, #write h4, #write h5, #write h6, #write p { position: relative; }
p { line-height: inherit; }
h1, h2, h3, h4, h5, h6 { break-after: avoid-page; break-inside: avoid; orphans: 4; }
p { orphans: 4; }
h1 { font-size: 2rem; }
h2 { font-size: 1.8rem; }
h3 { font-size: 1.6rem; }
h4 { font-size: 1.4rem; }
h5 { font-size: 1.2rem; }
h6 { font-size: 1rem; }
.md-math-block, .md-rawblock, h1, h2, h3, h4, h5, h6, p { margin-top: 1rem; margin-bottom: 1rem; }
.hidden { display: none; }
.md-blockmeta { color: rgb(204, 204, 204); font-weight: 700; font-style: italic; }
a { cursor: pointer; }
sup.md-footnote { padding: 2px 4px; background-color: rgba(238, 238, 238, 0.7); color: rgb(85, 85, 85); border-radius: 4px; cursor: pointer; }
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#write input[type="checkbox"] { cursor: pointer; width: inherit; height: inherit; }
figure { overflow-x: auto; margin: 1.2em 0px; max-width: calc(100% + 16px); padding: 0px; }
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tr { break-inside: avoid; break-after: auto; }
thead { display: table-header-group; }
table { border-collapse: collapse; border-spacing: 0px; width: 100%; overflow: auto; break-inside: auto; text-align: left; }
table.md-table td { min-width: 32px; }
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#write pre.ty-contain-cm { white-space: normal; }
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.md-fences.mock-cm.md-fences-with-lineno { padding-left: 8px; }
.CodeMirror-line, twitterwidget { break-inside: avoid; }
.footnotes { opacity: 0.8; font-size: 0.9rem; margin-top: 1em; margin-bottom: 1em; }
.footnotes + .footnotes { margin-top: 0px; }
.md-reset { margin: 0px; padding: 0px; border: 0px; outline: 0px; vertical-align: top; background: 0px 0px; text-decoration: none; text-shadow: none; float: none; position: static; width: auto; height: auto; white-space: nowrap; cursor: inherit; -webkit-tap-highlight-color: transparent; line-height: normal; font-weight: 400; text-align: left; box-sizing: content-box; direction: ltr; }
li div { padding-top: 0px; }
blockquote { margin: 1rem 0px; }
li .mathjax-block, li p { margin: 0.5rem 0px; }
li blockquote { margin: 1rem 0px; }
li { margin: 0px; position: relative; }
blockquote > :last-child { margin-bottom: 0px; }
blockquote > :first-child, li > :first-child { margin-top: 0px; }
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}
.footnote-line { margin-top: 0.714em; font-size: 0.7em; }
a img, img a { cursor: pointer; }
pre.md-meta-block { font-size: 0.8rem; min-height: 0.8rem; white-space: pre-wrap; background: rgb(204, 204, 204); display: block; overflow-x: hidden; }
p > .md-image:only-child:not(.md-img-error) img, p > img:only-child { display: block; margin: auto; }
#write.first-line-indent p > .md-image:only-child:not(.md-img-error) img { left: -2em; position: relative; }
p > .md-image:only-child { display: inline-block; width: 100%; }
#write .MathJax_Display { margin: 0.8em 0px 0px; }
.md-math-block { width: 100%; }
.md-math-block:not(:empty)::after { display: none; }
.MathJax_ref { fill: currentcolor; }
[contenteditable="true"]:active, [contenteditable="true"]:focus, [contenteditable="false"]:active, [contenteditable="false"]:focus { outline: 0px; box-shadow: none; }
.md-task-list-item { position: relative; list-style-type: none; }
.task-list-item.md-task-list-item { padding-left: 0px; }
.md-task-list-item > input { position: absolute; top: 0px; left: 0px; margin-left: -1.2em; margin-top: calc(1em - 10px); border: none; }
.math { font-size: 1rem; }
.md-toc { min-height: 3.58rem; position: relative; font-size: 0.9rem; border-radius: 10px; }
.md-toc-content { position: relative; margin-left: 0px; }
.md-toc-content::after, .md-toc::after { display: none; }
.md-toc-item { display: block; color: rgb(65, 131, 196); }
.md-toc-item a { text-decoration: none; }
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.md-toc-h2 .md-toc-inner { margin-left: 2em; }
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.md-toc-h4 .md-toc-inner { margin-left: 6em; }
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  .md-toc-h6 .md-toc-inner { margin-left: 8em; }
}
a.md-toc-inner { font-size: inherit; font-style: inherit; font-weight: inherit; line-height: inherit; }
.footnote-line a:not(.reversefootnote) { color: inherit; }
.md-attr { display: none; }
.md-fn-count::after { content: "."; }
code, pre, samp, tt { font-family: var(--monospace); }
kbd { margin: 0px 0.1em; padding: 0.1em 0.6em; font-size: 0.8em; color: rgb(36, 39, 41); background: rgb(255, 255, 255); border: 1px solid rgb(173, 179, 185); border-radius: 3px; box-shadow: rgba(12, 13, 14, 0.2) 0px 1px 0px, rgb(255, 255, 255) 0px 0px 0px 2px inset; white-space: nowrap; vertical-align: middle; }
.md-comment { color: rgb(162, 127, 3); opacity: 0.8; font-family: var(--monospace); }
code { text-align: left; vertical-align: initial; }
a.md-print-anchor { white-space: pre !important; border-width: initial !important; border-style: none !important; border-color: initial !important; display: inline-block !important; position: absolute !important; width: 1px !important; right: 0px !important; outline: 0px !important; background: 0px 0px !important; text-decoration: initial !important; text-shadow: initial !important; }
.os-windows.monocolor-emoji .md-emoji { font-family: "Segoe UI Symbol", sans-serif; }
.md-diagram-panel > svg { max-width: 100%; }
[lang="flow"] svg, [lang="mermaid"] svg { max-width: 100%; height: auto; }
[lang="mermaid"] .node text { font-size: 1rem; }
table tr th { border-bottom: 0px; }
video { max-width: 100%; display: block; margin: 0px auto; }
iframe { max-width: 100%; width: 100%; border: none; }
.highlight td, .highlight tr { border: 0px; }
mark { background: rgb(255, 255, 0); color: rgb(0, 0, 0); }
.md-html-inline .md-plain, .md-html-inline strong, mark .md-inline-math, mark strong { color: inherit; }
.md-expand mark .md-meta { opacity: 0.3 !important; }
mark .md-meta { color: rgb(0, 0, 0); }
@media print {
  .typora-export h1, .typora-export h2, .typora-export h3, .typora-export h4, .typora-export h5, .typora-export h6 { break-inside: avoid; }
}
.md-diagram-panel .messageText { stroke: none !important; }
.md-diagram-panel .start-state { fill: var(--node-fill); }
.md-diagram-panel .edgeLabel rect { opacity: 1 !important; }
.md-require-zoom-fix { height: auto; margin-top: 16px; margin-bottom: 16px; }
.md-require-zoom-fix foreignobject { font-size: var(--mermaid-font-zoom); }
.md-fences.md-fences-math { font-size: 1em; }
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.md-fences-advanced:not(.md-focus) { background: inherit; }
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.typora-export-show-outline #write { --webkit-flex:2; flex: 2 1 0%; }
.typora-export-sidebar .outline-content { position: fixed; top: 0px; max-height: 100%; overflow: hidden auto; padding-bottom: 30px; padding-top: 60px; width: 300px; }
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@media screen and (max-width: 800px) {
  .typora-export-sidebar { display: none; }
}
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.outline-content ul { margin-top: 0px; margin-bottom: 0px; }
.outline-content strong { font-weight: 400; }
.outline-expander { width: 1rem; height: 1.42857rem; position: relative; display: table-cell; vertical-align: middle; cursor: pointer; padding-left: 4px; }
.outline-expander::before { content: ""; position: relative; font-family: Ionicons; display: inline-block; font-size: 8px; vertical-align: middle; }
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:root {
    --side-bar-bg-color: #fafafa;
    --control-text-color: #777;
}

@include-when-export url(https://fonts.loli.net/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext);

/* open-sans-regular - latin-ext_latin */
  /* open-sans-italic - latin-ext_latin */
    /* open-sans-700 - latin-ext_latin */
    /* open-sans-700italic - latin-ext_latin */
  html {
    font-size: 16px;
    -webkit-font-smoothing: antialiased;
}

body {
    font-family: "Open Sans","Clear Sans", "Helvetica Neue", Helvetica, Arial, 'Segoe UI Emoji', sans-serif;
    color: rgb(51, 51, 51);
    line-height: 1.6;
}

#write {
    max-width: 860px;
  	margin: 0 auto;
  	padding: 30px;
    padding-bottom: 100px;
}

@media only screen and (min-width: 1400px) {
	#write {
		max-width: 1024px;
	}
}

@media only screen and (min-width: 1800px) {
	#write {
		max-width: 1200px;
	}
}

#write > ul:first-child,
#write > ol:first-child{
    margin-top: 30px;
}

a {
    color: #4183C4;
}
h1,
h2,
h3,
h4,
h5,
h6 {
    position: relative;
    margin-top: 1rem;
    margin-bottom: 1rem;
    font-weight: bold;
    line-height: 1.4;
    cursor: text;
}
h1:hover a.anchor,
h2:hover a.anchor,
h3:hover a.anchor,
h4:hover a.anchor,
h5:hover a.anchor,
h6:hover a.anchor {
    text-decoration: none;
}
h1 tt,
h1 code {
    font-size: inherit;
}
h2 tt,
h2 code {
    font-size: inherit;
}
h3 tt,
h3 code {
    font-size: inherit;
}
h4 tt,
h4 code {
    font-size: inherit;
}
h5 tt,
h5 code {
    font-size: inherit;
}
h6 tt,
h6 code {
    font-size: inherit;
}
h1 {
    font-size: 2.25em;
    line-height: 1.2;
    border-bottom: 1px solid #eee;
}
h2 {
    font-size: 1.75em;
    line-height: 1.225;
    border-bottom: 1px solid #eee;
}

/*@media print {
    .typora-export h1,
    .typora-export h2 {
        border-bottom: none;
        padding-bottom: initial;
    }

    .typora-export h1::after,
    .typora-export h2::after {
        content: "";
        display: block;
        height: 100px;
        margin-top: -96px;
        border-top: 1px solid #eee;
    }
}*/

h3 {
    font-size: 1.5em;
    line-height: 1.43;
}
h4 {
    font-size: 1.25em;
}
h5 {
    font-size: 1em;
}
h6 {
   font-size: 1em;
    color: #777;
}
p,
blockquote,
ul,
ol,
dl,
table{
    margin: 0.8em 0;
}
li>ol,
li>ul {
    margin: 0 0;
}
hr {
    height: 2px;
    padding: 0;
    margin: 16px 0;
    background-color: #e7e7e7;
    border: 0 none;
    overflow: hidden;
    box-sizing: content-box;
}

li p.first {
    display: inline-block;
}
ul,
ol {
    padding-left: 30px;
}
ul:first-child,
ol:first-child {
    margin-top: 0;
}
ul:last-child,
ol:last-child {
    margin-bottom: 0;
}
blockquote {
    border-left: 4px solid #dfe2e5;
    padding: 0 15px;
    color: #777777;
}
blockquote blockquote {
    padding-right: 0;
}
table {
    padding: 0;
    word-break: initial;
}
table tr {
    border: 1px solid #dfe2e5;
    margin: 0;
    padding: 0;
}
table tr:nth-child(2n),
thead {
    background-color: #f8f8f8;
}
table th {
    font-weight: bold;
    border: 1px solid #dfe2e5;
    border-bottom: 0;
    margin: 0;
    padding: 6px 13px;
}
table td {
    border: 1px solid #dfe2e5;
    margin: 0;
    padding: 6px 13px;
}
table th:first-child,
table td:first-child {
    margin-top: 0;
}
table th:last-child,
table td:last-child {
    margin-bottom: 0;
}

.CodeMirror-lines {
    padding-left: 4px;
}

.code-tooltip {
    box-shadow: 0 1px 1px 0 rgba(0,28,36,.3);
    border-top: 1px solid #eef2f2;
}

.md-fences,
code,
tt {
    border: 1px solid #e7eaed;
    background-color: #f8f8f8;
    border-radius: 3px;
    padding: 0;
    padding: 2px 4px 0px 4px;
    font-size: 0.9em;
}

code {
    background-color: #f3f4f4;
    padding: 0 2px 0 2px;
}

.md-fences {
    margin-bottom: 15px;
    margin-top: 15px;
    padding-top: 8px;
    padding-bottom: 6px;
}


.md-task-list-item > input {
  margin-left: -1.3em;
}

@media print {
    html {
        font-size: 13px;
    }
    table,
    pre {
        page-break-inside: avoid;
    }
    pre {
        word-wrap: break-word;
    }
}

.md-fences {
	background-color: #f8f8f8;
}
#write pre.md-meta-block {
	padding: 1rem;
    font-size: 85%;
    line-height: 1.45;
    background-color: #f7f7f7;
    border: 0;
    border-radius: 3px;
    color: #777777;
    margin-top: 0 !important;
}

.mathjax-block>.code-tooltip {
	bottom: .375rem;
}

.md-mathjax-midline {
    background: #fafafa;
}

#write>h3.md-focus:before{
	left: -1.5625rem;
	top: .375rem;
}
#write>h4.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
#write>h5.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
#write>h6.md-focus:before{
	left: -1.5625rem;
	top: .285714286rem;
}
.md-image>.md-meta {
    /*border: 1px solid #ddd;*/
    border-radius: 3px;
    padding: 2px 0px 0px 4px;
    font-size: 0.9em;
    color: inherit;
}

.md-tag {
    color: #a7a7a7;
    opacity: 1;
}

.md-toc { 
    margin-top:20px;
    padding-bottom:20px;
}

.sidebar-tabs {
    border-bottom: none;
}

#typora-quick-open {
    border: 1px solid #ddd;
    background-color: #f8f8f8;
}

#typora-quick-open-item {
    background-color: #FAFAFA;
    border-color: #FEFEFE #e5e5e5 #e5e5e5 #eee;
    border-style: solid;
    border-width: 1px;
}

/** focus mode */
.on-focus-mode blockquote {
    border-left-color: rgba(85, 85, 85, 0.12);
}

header, .context-menu, .megamenu-content, footer{
    font-family: "Segoe UI", "Arial", sans-serif;
}

.file-node-content:hover .file-node-icon,
.file-node-content:hover .file-node-open-state{
    visibility: visible;
}

.mac-seamless-mode #typora-sidebar {
    background-color: #fafafa;
    background-color: var(--side-bar-bg-color);
}

.md-lang {
    color: #b4654d;
}

/*.html-for-mac {
    --item-hover-bg-color: #E6F0FE;
}*/

#md-notification .btn {
    border: 0;
}

.dropdown-menu .divider {
    border-color: #e5e5e5;
    opacity: 0.4;
}

.ty-preferences .window-content {
    background-color: #fafafa;
}

.ty-preferences .nav-group-item.active {
    color: white;
    background: #999;
}

.menu-item-container a.menu-style-btn {
    background-color: #f5f8fa;
    background-image: linear-gradient( 180deg , hsla(0, 0%, 100%, 0.8), hsla(0, 0%, 100%, 0)); 
}



mjx-container[jax="SVG"] {
  direction: ltr;
}

mjx-container[jax="SVG"] > svg {
  overflow: visible;
  min-height: 1px;
  min-width: 1px;
}

mjx-container[jax="SVG"] > svg a {
  fill: blue;
  stroke: blue;
}

mjx-assistive-mml {
  position: absolute !important;
  top: 0px;
  left: 0px;
  clip: rect(1px, 1px, 1px, 1px);
  padding: 1px 0px 0px 0px !important;
  border: 0px !important;
  display: block !important;
  width: auto !important;
  overflow: hidden !important;
  -webkit-touch-callout: none;
  -webkit-user-select: none;
  -khtml-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}

mjx-assistive-mml[display="block"] {
  width: 100% !important;
}

mjx-container[jax="SVG"][display="true"] {
  display: block;
  text-align: center;
  margin: 1em 0;
}

mjx-container[jax="SVG"][display="true"][width="full"] {
  display: flex;
}

mjx-container[jax="SVG"][justify="left"] {
  text-align: left;
}

mjx-container[jax="SVG"][justify="right"] {
  text-align: right;
}

g[data-mml-node="merror"] > g {
  fill: red;
  stroke: red;
}

g[data-mml-node="merror"] > rect[data-background] {
  fill: yellow;
  stroke: none;
}

g[data-mml-node="mtable"] > line[data-line], svg[data-table] > g > line[data-line] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {
  stroke-dasharray: 140;
}

g[data-mml-node="mtable"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {
  stroke-linecap: round;
  stroke-dasharray: 0,140;
}

g[data-mml-node="mtable"] > g > svg {
  overflow: visible;
}

[jax="SVG"] mjx-tool {
  display: inline-block;
  position: relative;
  width: 0;
  height: 0;
}

[jax="SVG"] mjx-tool > mjx-tip {
  position: absolute;
  top: 0;
  left: 0;
}

mjx-tool > mjx-tip {
  display: inline-block;
  padding: .2em;
  border: 1px solid #888;
  font-size: 70%;
  background-color: #F8F8F8;
  color: black;
  box-shadow: 2px 2px 5px #AAAAAA;
}

g[data-mml-node="maction"][data-toggle] {
  cursor: pointer;
}

mjx-status {
  display: block;
  position: fixed;
  left: 1em;
  bottom: 1em;
  min-width: 25%;
  padding: .2em .4em;
  border: 1px solid #888;
  font-size: 90%;
  background-color: #F8F8F8;
  color: black;
}

foreignObject[data-mjx-xml] {
  font-family: initial;
  line-height: normal;
  overflow: visible;
}

mjx-container[jax="SVG"] path[data-c], mjx-container[jax="SVG"] use[data-c] {
  stroke-width: 3;
}

g[data-mml-node="xypic"] path {
  stroke-width: inherit;
}

.MathJax g[data-mml-node="xypic"] path {
  stroke-width: inherit;
}
mjx-container[jax="SVG"] path[data-c], mjx-container[jax="SVG"] use[data-c] {
							stroke-width: 0;
						}
</style><title>0021 line search</title>
</head>
<body class='typora-export os-windows'><div class='typora-export-content'>
<div id='write'  class=''><p><span>line search</span></p><p><a href='https://zhuanlan.zhihu.com/p/90758617' target='_blank' class='url'>https://zhuanlan.zhihu.com/p/90758617</a></p><p>&nbsp;</p><p><span>优化问题的基本形式：</span></p><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="16.738ex" height="2.041ex" role="img" focusable="false" viewBox="0 -694 7398.3 902" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.471ex;"><defs><path id="MJX-28-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-28-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-28-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-28-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-28-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-28-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-28-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-28-TEX-I-1D465"></use></g><g data-mml-node="TeXAtom" transform="translate(605,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D458" xlink:href="#MJX-28-TEX-I-1D458"></use></g><g data-mml-node="mo" transform="translate(521,0)"><use data-c="2B" xlink:href="#MJX-28-TEX-N-2B"></use></g><g data-mml-node="mn" transform="translate(1299,0)"><use data-c="31" xlink:href="#MJX-28-TEX-N-31"></use></g></g></g><g data-mml-node="mo" transform="translate(2204.9,0)"><use data-c="3D" xlink:href="#MJX-28-TEX-N-3D"></use></g><g data-mml-node="msub" transform="translate(3260.6,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-28-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-28-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(4506.3,0)"><use data-c="2B" xlink:href="#MJX-28-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(5506.5,0)"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-28-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(502,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-28-TEX-I-1D458"></use></g></g><g data-mml-node="msub" transform="translate(6426.9,0)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-28-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-28-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>s</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">x_{k+1} = x_k + s_kd_k</script></p><ul><li><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.082ex" height="1.357ex" role="img" focusable="false" viewBox="0 -442 920.4 599.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-29-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path><path id="MJX-29-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-29-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(502,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-29-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">s_k</script><span>为步长</span></li><li><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.198ex" height="1.927ex" role="img" focusable="false" viewBox="0 -694 971.4 851.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-34-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-34-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-34-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-34-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>d</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">d_k</script><span>为方向</span></li></ul><p>&nbsp;</p><p><span>方向需要满足的条件：</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n12" cid="n12" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="14.613ex" height="2.583ex" role="img" focusable="false" viewBox="0 -891.7 6459.2 1141.7" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-1-TEX-V-25BD" d="M84 556Q84 567 99 576H622Q637 567 637 556Q637 551 572 409T441 127T375 -14Q368 -19 360 -19H358Q349 -19 342 -7T296 92Q249 193 211 275Q84 550 84 556ZM586 534Q586 536 361 536Q135 536 135 535L358 52L361 47L473 290Q584 532 586 534Z"></path><path id="MJX-1-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-1-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-1-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-1-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 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stretchy="false">↓</mo><mn>0</mn></mrow></msub><mtext>&nbsp;</mtext><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>+</mo><mi>s</mi><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>s</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container></div></div><ul><li><p><span>当s足够小时</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n20" cid="n20" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="34.995ex" height="2.583ex" role="img" focusable="false" viewBox="0 -891.7 15467.7 1141.7" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-3-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-3-TEX-N-28" d="M94 250Q94 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336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-3-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-3-TEX-I-1D453"></use></g><g data-mml-node="mo" transform="translate(550,0)"><use data-c="28" xlink:href="#MJX-3-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(939,0)"><g data-mml-node="mi"><use 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data-c="28" xlink:href="#MJX-3-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(10941,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-3-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-3-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(12186.6,0)"><use data-c="2B" xlink:href="#MJX-3-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(13186.9,0)"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-3-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(502,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-3-TEX-I-1D458"></use></g></g><g data-mml-node="msub" transform="translate(14107.3,0)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-3-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-3-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(15078.7,0)"><use data-c="29" xlink:href="#MJX-3-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>+</mo><mi>s</mi><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>s</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container></div></div></li><li><p><span>所以，想要</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="20.703ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 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data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-5-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-5-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(19623,0)"><use data-c="29" xlink:href="#MJX-5-TEX-N-29"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable rowspacing=".5em" columnspacing="1em" displaystyle="true"><mtr><mtd><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>≤</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>c</mi><mn>1</mn></msub><msub><mi>α</mi><mi>k</mi></msub><mi data-mjx-alternate="1">▽</mi><msubsup><mi>f</mi><mi>k</mi><mi>T</mi></msubsup><msub><mi>d</mi><mi>k</mi></msub><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><mo>,</mo><mn>0</mn><mo>&lt;</mo><msub><mi>c</mi><mn>1</mn></msub><mo>&lt;</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>∵</mo><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>∴</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>≤</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>c</mi><mn>1</mn></msub><msub><mi>α</mi><mi>k</mi></msub><mi data-mjx-alternate="1">▽</mi><msubsup><mi>f</mi><mi>k</mi><mi>T</mi></msubsup><msub><mi>d</mi><mi>k</mi></msub><mo>&lt;</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><ul><li><p><span>因为当</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.315ex" height="1.357ex" role="img" focusable="false" viewBox="0 -442 1023.4 599.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-33-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-33-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-33-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-33-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">x_k</script><span>和</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.198ex" height="1.927ex" role="img" focusable="false" viewBox="0 -694 971.4 851.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-34-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path><path id="MJX-34-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-34-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-34-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>d</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">d_k</script><span>确定时，只有</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.469ex" height="1.357ex" role="img" focusable="false" viewBox="0 -442 1091.4 599.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-35-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-35-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-35-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-35-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha_k</script><span>为变量，上式修改为：</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n37" cid="n37" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="26.952ex" height="9.405ex" role="img" focusable="false" viewBox="0 -2328.6 11913 4157.2" 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261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-6-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 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359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-6-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-6-TEX-V-25BD" d="M84 556Q84 567 99 576H622Q637 567 637 556Q637 551 572 409T441 127T375 -14Q368 -19 360 -19H358Q349 -19 342 -7T296 92Q249 193 211 275Q84 550 84 556ZM586 534Q586 536 361 536Q135 536 135 535L358 52L361 47L473 290Q584 532 586 534Z"></path><path id="MJX-6-TEX-I-1D447" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,1578.6)"><g data-mml-node="mtd" transform="translate(3036.8,0)"><g data-mml-node="mi"><use data-c="1D703" xlink:href="#MJX-6-TEX-I-1D703"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(858,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-6-TEX-I-1D6FC"></use></g><g data-mml-node="mi" 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transform="translate(0,78.6)"><g data-mml-node="mtd" transform="translate(1302.2,0)"><g data-mml-node="mi"><use data-c="1D703" xlink:href="#MJX-6-TEX-I-1D703"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(858,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-6-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1949.4,0)"><use data-c="29" xlink:href="#MJX-6-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2616.2,0)"><use data-c="3D" xlink:href="#MJX-6-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(3672,0)"><use data-c="1D453" xlink:href="#MJX-6-TEX-I-1D453"></use></g><g data-mml-node="mo" transform="translate(4222,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g 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xlink:href="#MJX-6-TEX-N-29"></use></g></g></g><g data-mml-node="mtr" transform="translate(0,-1563.1)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D459" xlink:href="#MJX-6-TEX-I-1D459"></use></g><g data-mml-node="mo" transform="translate(298,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(687,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-6-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1778.4,0)"><use data-c="29" xlink:href="#MJX-6-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2445.2,0)"><use data-c="3D" xlink:href="#MJX-6-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(3501,0)"><use data-c="1D453" xlink:href="#MJX-6-TEX-I-1D453"></use></g><g data-mml-node="mo" transform="translate(4051,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(4440,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-6-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(5463.4,0)"><use data-c="29" xlink:href="#MJX-6-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(6074.6,0)"><use data-c="2B" xlink:href="#MJX-6-TEX-N-2B"></use></g><g data-mml-node="msub" transform="translate(7074.8,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-6-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-6-TEX-N-31"></use></g></g><g data-mml-node="msub" transform="translate(7944.4,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-6-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g><g data-mml-node="mi" transform="translate(9035.8,0)"><use data-c="25BD" xlink:href="#MJX-6-TEX-V-25BD"></use></g><g data-mml-node="msubsup" transform="translate(9757.8,0)"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-6-TEX-I-1D453"></use></g><g data-mml-node="mi" transform="translate(636,413) scale(0.707)"><use data-c="1D447" xlink:href="#MJX-6-TEX-I-1D447"></use></g><g data-mml-node="mi" transform="translate(523,-257.7) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g><g data-mml-node="msub" transform="translate(10941.6,0)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-6-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-6-TEX-I-1D458"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable rowspacing=".5em" columnspacing="1em" displaystyle="true"><mtr><mtd><mi>θ</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>≤</mo><mi>l</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>θ</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>l</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>c</mi><mn>1</mn></msub><msub><mi>α</mi><mi>k</mi></msub><mi data-mjx-alternate="1">▽</mi><msubsup><mi>f</mi><mi>k</mi><mi>T</mi></msubsup><msub><mi>d</mi><mi>k</mi></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div></li><li><p><span>理解：</span></p><ul><li><p><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.904ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2167.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-43-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-43-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-43-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-43-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-43-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D459" xlink:href="#MJX-43-TEX-I-1D459"></use></g><g data-mml-node="mo" transform="translate(298,0)"><use data-c="28" xlink:href="#MJX-43-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(687,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-43-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-43-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1778.4,0)"><use data-c="29" xlink:href="#MJX-43-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">l(\alpha_k)</script><span>和y轴的交点为</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.32ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2351.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-45-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-45-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-45-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-45-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-45-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-45-TEX-I-1D453"></use></g><g data-mml-node="mo" transform="translate(550,0)"><use data-c="28" xlink:href="#MJX-45-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(939,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-45-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-45-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1962.4,0)"><use data-c="29" xlink:href="#MJX-45-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">f(x_k)</script><span>，斜率为</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="8.477ex" height="2.618ex" role="img" focusable="false" viewBox="0 -841.7 3746.8 1157.2" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.714ex;"><defs><path id="MJX-38-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path><path id="MJX-38-TEX-N-31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path id="MJX-38-TEX-V-25BD" d="M84 556Q84 567 99 576H622Q637 567 637 556Q637 551 572 409T441 127T375 -14Q368 -19 360 -19H358Q349 -19 342 -7T296 92Q249 193 211 275Q84 550 84 556ZM586 534Q586 536 361 536Q135 536 135 535L358 52L361 47L473 290Q584 532 586 534Z"></path><path id="MJX-38-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 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353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-38-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-38-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-38-TEX-N-31"></use></g></g><g data-mml-node="mi" transform="translate(869.6,0)"><use data-c="25BD" xlink:href="#MJX-38-TEX-V-25BD"></use></g><g data-mml-node="msubsup" transform="translate(1591.6,0)"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-38-TEX-I-1D453"></use></g><g data-mml-node="mi" transform="translate(636,363) scale(0.707)"><use data-c="1D447" xlink:href="#MJX-38-TEX-I-1D447"></use></g><g data-mml-node="mi" transform="translate(523,-307.7) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-38-TEX-I-1D458"></use></g></g><g data-mml-node="msub" transform="translate(2775.4,0)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-38-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-38-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub><mi data-mjx-alternate="1">▽</mi><msubsup><mi>f</mi><mi>k</mi><mi>T</mi></msubsup><msub><mi>d</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">c_1\triangledown f_k^Td_k</script></p></li><li><p><span>根据下式，</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.291ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2338.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-44-TEX-I-1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z"></path><path id="MJX-44-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-44-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-44-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-44-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D703" xlink:href="#MJX-44-TEX-I-1D703"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-44-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(858,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-44-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-44-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1949.4,0)"><use data-c="29" xlink:href="#MJX-44-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">\theta(\alpha_k)</script><span>在</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="6.618ex" height="1.864ex" role="img" focusable="false" viewBox="0 -666 2925 823.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-40-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-40-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-40-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-40-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-40-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-40-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1369.2,0)"><use data-c="3D" xlink:href="#MJX-40-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(2425,0)"><use data-c="30" xlink:href="#MJX-40-TEX-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>k</mi></msub><mo>=</mo><mn>0</mn></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha_k=0</script><span>处，斜率为</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.667ex" height="1.927ex" role="img" focusable="false" viewBox="0 -694 2062.8 851.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-41-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-41-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-41-TEX-I-1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-41-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-41-TEX-I-1D458"></use></g></g><g data-mml-node="msub" transform="translate(1091.4,0)"><g data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-41-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-41-TEX-I-1D458"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha_kd_k</script><span>，且和y轴相交为</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.32ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2351.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-45-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-45-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 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data-mml-node="mi"><use data-c="1D451" xlink:href="#MJX-7-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(553,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-7-TEX-I-1D458"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable rowspacing=".5em" columnspacing="1em" displaystyle="true"><mtr><mtd><mfrac><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><msub><mi>α</mi><mi>k</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><mi>z</mi></mrow></mfrac><mfrac><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><mi>z</mi></mrow><mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-auto-op="false" mathvariant="normal">d</mi></mrow><msub><mi>α</mi><mi>k</mi></msub></mrow></mfrac><mo>=</mo><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>,</mo><mi>z</mi><mo>=</mo><msub><mi>x</mi><mi>k</mi></msub><mo>+</mo><msub><mi>α</mi><mi>k</mi></msub><msub><mi>d</mi><mi>k</mi></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div></li><li><p><span>所以</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="4.904ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2167.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-43-TEX-I-1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path><path id="MJX-43-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-43-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-43-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-43-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D459" xlink:href="#MJX-43-TEX-I-1D459"></use></g><g data-mml-node="mo" transform="translate(298,0)"><use data-c="28" xlink:href="#MJX-43-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(687,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-43-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-43-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1778.4,0)"><use data-c="29" xlink:href="#MJX-43-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">l(\alpha_k)</script><span>和</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.291ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2338.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-44-TEX-I-1D703" d="M35 200Q35 302 74 415T180 610T319 704Q320 704 327 704T339 705Q393 701 423 656Q462 596 462 495Q462 380 417 261T302 66T168 -10H161Q125 -10 99 10T60 63T41 130T35 200ZM383 566Q383 668 330 668Q294 668 260 623T204 521T170 421T157 371Q206 370 254 370L351 371Q352 372 359 404T375 484T383 566ZM113 132Q113 26 166 26Q181 26 198 36T239 74T287 161T335 307L340 324H145Q145 321 136 286T120 208T113 132Z"></path><path id="MJX-44-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-44-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-44-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-44-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D703" xlink:href="#MJX-44-TEX-I-1D703"></use></g><g data-mml-node="mo" transform="translate(469,0)"><use data-c="28" xlink:href="#MJX-44-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(858,0)"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-44-TEX-I-1D6FC"></use></g><g data-mml-node="mi" transform="translate(673,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-44-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1949.4,0)"><use data-c="29" xlink:href="#MJX-44-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">\theta(\alpha_k)</script><span>相交于</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="5.32ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2351.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-45-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-45-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-45-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-45-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-45-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-45-TEX-I-1D453"></use></g><g data-mml-node="mo" transform="translate(550,0)"><use data-c="28" xlink:href="#MJX-45-TEX-N-28"></use></g><g data-mml-node="msub" transform="translate(939,0)"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-45-TEX-I-1D465"></use></g><g data-mml-node="mi" transform="translate(605,-150) scale(0.707)"><use data-c="1D458" xlink:href="#MJX-45-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(1962.4,0)"><use data-c="29" xlink:href="#MJX-45-TEX-N-29"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container><script type="math/tex">f(x_k)</script><span>，且前者在后者上方（斜率比后者小）</span></p></li><li><p><img src="http://www.52nlp.cn/images/opt2-4.png" referrerpolicy="no-referrer" alt="img"></p></li></ul></li></ul><p>&nbsp;</p><p><span>condition2：为了保证</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="18.968ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 8384 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-46-TEX-V-25BD" d="M84 556Q84 567 99 576H622Q637 567 637 556Q637 551 572 409T441 127T375 -14Q368 -19 360 -19H358Q349 -19 342 -7T296 92Q249 193 211 275Q84 550 84 556ZM586 534Q586 536 361 536Q135 536 135 535L358 52L361 47L473 290Q584 532 586 534Z"></path><path id="MJX-46-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path><path id="MJX-46-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-46-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-46-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-46-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-46-TEX-N-31" d="M213 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xlink:href="#MJX-8-TEX-I-1D458"></use></g></g><g data-mml-node="mo" transform="translate(12358,0)"><use data-c="2C" xlink:href="#MJX-8-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(12802.7,0)"><use data-c="30" xlink:href="#MJX-8-TEX-N-30"></use></g><g data-mml-node="mo" transform="translate(13580.5,0)"><use data-c="3C" xlink:href="#MJX-8-TEX-N-3C"></use></g><g data-mml-node="msub" transform="translate(14636.2,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-8-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="31" xlink:href="#MJX-8-TEX-N-31"></use></g></g><g data-mml-node="mo" transform="translate(15783.6,0)"><use data-c="3C" xlink:href="#MJX-8-TEX-N-3C"></use></g><g data-mml-node="msub" transform="translate(16839.3,0)"><g data-mml-node="mi"><use data-c="1D450" xlink:href="#MJX-8-TEX-I-1D450"></use></g><g data-mml-node="mn" transform="translate(466,-150) scale(0.707)"><use data-c="32" xlink:href="#MJX-8-TEX-N-32"></use></g></g><g data-mml-node="mo" transform="translate(17986.7,0)"><use data-c="3C" xlink:href="#MJX-8-TEX-N-3C"></use></g><g data-mml-node="mn" transform="translate(19042.4,0)"><use data-c="31" xlink:href="#MJX-8-TEX-N-31"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>≥</mo><msub><mi>c</mi><mn>2</mn></msub><mi data-mjx-alternate="1">▽</mi><mi>f</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><msup><mo stretchy="false">)</mo><mi>T</mi></msup><msub><mi>d</mi><mi>k</mi></msub><mo>,</mo><mn>0</mn><mo>&lt;</mo><msub><mi>c</mi><mn>1</mn></msub><mo>&lt;</mo><msub><mi>c</mi><mn>2</mn></msub><mo>&lt;</mo><mn>1</mn></math></mjx-assistive-mml></mjx-container></div></div><p>&nbsp;</p><p><span>完整算法：</span></p><ol><li><p><span>根据条件1，确定下降的大概范围</span></p><ul><li><span>从</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.436ex" height="1.375ex" role="img" focusable="false" viewBox="0 -442 1076.6 607.6" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-55-TEX-I-1D6FC" d="M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z"></path><path id="MJX-55-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D6FC" xlink:href="#MJX-55-TEX-I-1D6FC"></use></g><g data-mml-node="mn" transform="translate(673,-150) scale(0.707)"><use data-c="30" xlink:href="#MJX-55-TEX-N-30"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>α</mi><mn>0</mn></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">\alpha_0</script><span>开始，每次加一定值一直试，知道不满足，得到边界</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="2.344ex" height="1.355ex" role="img" focusable="false" viewBox="0 -441 1036.3 598.8" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-61-TEX-I-1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path><path id="MJX-61-TEX-I-1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D44E" xlink:href="#MJX-61-TEX-I-1D44E"></use></g><g data-mml-node="mi" transform="translate(562,-150) scale(0.707)"><use data-c="1D45B" xlink:href="#MJX-61-TEX-I-1D45B"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mi>n</mi></msub></math></mjx-assistive-mml></mjx-container><script type="math/tex">a_n</script></li></ul></li></ol><ol start='2' ><li><span>通过两个边界，找满足条件2的</span></li></ol></div></div>
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